1. Field of the Invention
The present invention relates generally to a carrier-phase-based relative positioning device used in such apparatus as a global positioning system (GPS) compass which determines geographic direction from multiple relative position fixes obtained by using the phases of carrier signals received from GPS satellites or a real-time kinematic (RTK) GPS receiver which determines relative positions in real time by using the carrier phases of the GPS signals.
2. Description of the Prior Art
There exists a known method of determining relative positions by receiving radio signals transmitted from GPS satellites with multiple antennas and measuring the carrier phases of the signals. This method is conventionally used in an apparatus which determines relative positions of a mobile vehicle, such as a vessel.
Relative positions are determined in a manner described below in this kind of positioning apparatus.
A radio signal transmitted from one GPS satellite is received by multiple antennas and the phase of the carrier received by each antenna is determined. Then, using at least one pair of antennas, the difference between the phase of the carrier received by one antenna and the phase of the carrier received the by other antenna from the same GPS satellite (single phase difference) is determined. Alternatively, radio signals transmitted from two GPS satellites are received by multiple antennas and the phase of the carrier received by each antenna is determined. Then, using pairs of antennas, the difference between single phase differences obtained from the radio signals from the two GPS satellites (double phase difference) is determined. When the phase difference obtained by these methods is converted into the number of waves, the phase difference can be separated into an integral part and a fractional part. The fractional part of the phase difference can be directly measured by the measuring apparatus because it represents a value smaller than 2π in terms of carrier phase. It is however impossible to directly measure the integral part of the phase difference by the positioning apparatus. This integral part which is not directly measurable is referred to as integer bias, or ambiguity. It is possible to obtain a correct phase difference upon determining this ambiguity value. Relative positioning is made by calculating baseline vectors between a reference antenna and other antennas.
From a plurality of integer ambiguity values indirectly calculated, candidates of the potentially true integer ambiguity are obtained. Then, a single ambiguity value is selected through various verification processes and taken as the true integer ambiguity.
The aforementioned carrier-phase-based relative positioning device of the prior art has had problems shown below that should be overcome.
As stated above, the conventional carrier-phase-based relative positioning device determines carrier phase differences by constantly receiving radio signals from the same GPS satellite with multiple antennas. Each GPS satellite transmits radio waves containing a unique identification signal and the positioning device identifies and uses the radio waves transmitted from the same GPS satellite by reference to the identification signal. The carrier-phase-based relative positioning device calculates single or double phase differences upon receiving the radio waves from a specific GPS satellite in this way and determines the integer ambiguity and baseline vector based on these observations.
As long as continued reference is made to the radio waves transmitted from the same GPS satellite, the integer ambiguity does not vary with time. Thus, once an integer ambiguity value has been determined, it is possible to estimate the true integer ambiguity by reference to that integer ambiguity.
Since each GPS satellite orbits earth, however, its position varies with the lapse of time. Therefore, the angle of elevation of the GPS satellite varies from a high value to a low value, and vice versa. When the elevation of the GPS satellite varies from a high angle to an angle less than a specific value, it would become no longer possible to receive the radio waves transmitted from the GPS satellite with the antennas. On the other hand, when the elevation of the GPS satellite varies from a low angle to an angle above the specific value, the radio waves transmitted from the GPS satellite which could not been received by the antennas would become possible to receive from a particular point in time onward. For this reason, the number of GPS satellites from which the antennas can receive radio waves varies with the lapse of time
The carrier-phase-based relative positioning device normally calculates the integer ambiguity and baseline vector by reference to radio waves from as many GPS satellites as possible to obtain accurate position information. Therefore, if the number of satellites changes during the course of calculation, it is necessary to recalculate the integer ambiguity from the beginning. This is time-consuming and results in a waste of already accumulated data.
The aforementioned method of determining the integer ambiguity using the double phase difference requires a satellite to be used as a reference (hereinafter referred to as the reference satellite). In the double phase difference method, it becomes impossible to estimate the integer ambiguity value when it becomes impossible to receive radio waves from the reference satellite. When the elevation of the reference satellite becomes low, for example, it would become impossible for the antennas to receive the radio waves from the reference satellite, making it impossible to calculate the double phase difference. In such a case, it is necessary at that point in time to switch the reference satellite to another GPS satellite of which radio waves can be received by the antennas. Again, it becomes impossible in this case to continue estimation of the integer ambiguity value, making it necessary to recalculate the integer ambiguity from the beginning.
In verifying candidates of the potentially true integer ambiguity obtained as described above by the aforementioned conventional methods, there can arise a case where a wrong integer ambiguity value is chosen as the true integer ambiguity. This kind of error is likely to occur when the number of GPS satellites is small. Such errors could more or less occur in verifying the candidates of the true integer ambiguity no matter what kind of currently available verification process is used. The more stringent the verification process used in verifying the candidates of the true integer ambiguity, the more reliable the integer ambiguity obtained. A stringent verification process results in an extended measuring time, however. On the contrary, it would be possible to obtain a potentially true integer ambiguity in a short time if verification is carried out with somewhat broader range of permissible deviations. This, however, results in poorer accuracy. What is needed in carrier-phase-based relative positioning is a method of verifying the candidates of the potentially true integer ambiguity in a short time with a reduced possibility of errors.